(599ag) Uncertainty Relationship Analysis for Multi-Parametric Programming in Modeling and Optimization

In the progress of development of modeling and optimization for process design and operations problems under uncertainty, the process system engineering community has put more attention in the multi-parametric programming from the field of system theory and optimal control. This will help to achieve the full characterization of the entire range of solution space and provides a complete map of the various alternatives in the face of uncertainty.  

Uncertainty and variability exists in all levels of the industry operation and manufacturing because they are the inherent characterization of any process system. Up to now, all the research that handles with multi-parametric programming (mp-LP, mp-QP, mp-NLP, mp-MILP, mp-MINLP) treats the uncertainty parameters to be linearly independent with each other while actually there exist some kinds of quantitative relationship between each other. This area is lack of research while the relationship between these uncertainty parameters can help to reduce dimension of uncertainty space and provide the solution for multi-parametric programming with nonlinear uncertainty items appear in the constraints.

This paper presents the definition of multiple types of quantitative relationship between the uncertainty parameters which can be generalized into two classifications of strong relationship and weak relationship. The strong relationship can be used to reduce the dimension of uncertainty space while the weak relationship is used to reduce the region of search uncertainty space. With the combination of the above relationships, the scenarios will be provided to solve different kinds of multi-parametric programming which cannot be solved directly with historical research result.